Let ∗ be a binary operation on the set Q of rational numbers as follows:
a ∗ b = ab/4
Find which of the binary operations are commutative and which are associative.
Answers
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Step-by-step explanation:
Consider given the given binary operation,
a∗b=a
2
+b
2
Commutative-
a∗b=a
2
+b
2
b∗a=b
2
+a
2
a∗b=b∗a
Hence, given operation is commutative.
Associative –
a∗(b∗c)=a
2
∗(b
2
+c
2
)
=a
4
+(b
2
+c
2
)
2
(a∗b)∗c=(a
2
+b
2
)∗c
2
=(a
2
+b
2
)
2
+c
4
a∗(b∗c)
=(a∗b)∗c
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